Pre-Temporal Model of Quantum Causal Order

Adam Alzerkany

Hector E Mozo

We propose a theoretical framework in which time is not a fundamental variable but an emergentproperty arising from the transition between indefinite and definite causal order in quantum processes.Building on the process matrix formalism and the established phenomenon of indefinite causal order,we introduce the concept of Pre-Time, a fully quantum domain where no global temporal directionexists and causal relations remain in coherent superposition. Within this framework, we define acausal-emergence measure λ(W ) that quantifies the distance between a given process matrix W andthe convex set of causally separable processes; λ(W ) > 0 identifies genuinely pre-temporal systems,whereas λ(W ) = 0 corresponds to the emergence of a classical temporal order. We show that, underincreasing decoherence or environmental coupling, any physically realizable process must undergo amonotonic reduction of λ(W ), providing a mathematical mechanism for the conformation of temporalorder. Within this framework, apparent retrocausal paradoxes associated with delayed-choice andquantum eraser experiments do not arise, since the “past” is not a pre-existing entity but a structureformed only upon causal consolidation. The model remains fully consistent with quantum mechanics,relativity, and thermodynamic irreversibility, while offering novel predictions about intermediatepre-temporal phases and the emergence of classical causality. Our results suggest that time ariseswhen the universe selects a definite causal order, and that the pre-temporal quantum regime may playa central role in foundational physics and future quantum-gravity research.

Moses, Simon

This work investigates how temporal order and causal structure can emerge from quantum dynamics without assuming a pre-existing background notion of time. Pre­vious studies showed that asymmetric entanglement can generate internally coherent oscillations (”relational ticks”) that serve as a local, operational signature of time for the entangled subsystem. Here we extend this framework to address a fundamental question: can such locally generated ticks propagate to neighbouring systems?Using a minimal asymmetric two-qubit pair as the fundamental temporal element, we demonstrate two key results. The first is that entanglement asymmetry produces a stable internal beat frequency. The second is when these pairs are coupled along a finite quantum chain, the resulting temporal density propagates outward in a clear, finite-speed light-cone structure. Numerical simulations using a Lieb–Robinson style half-maximum criterion reveal a bounded signalling speed v∗, confirming that temporal influence spreads only within a causal cone.Importantly, this finite propagation speed arises directly from local quantum in­teractions and does not require any relativistic postulates, Lorentz symmetry, or a predefined time coordinate. In the coarse-grained limit, the temporal density exhibits wave-like behaviour with a characteristic speed approaching v∗, suggesting a pathway from microscopic entanglement asymmetry to macroscopic causal order.These results support a concrete mechanistic model in which time emerges from movement, causality emerges from locality, and a finite propagation speed arises nat­urally from asymmetric entanglement alone. This provides a plausible route by which relativistic causal structure may originate from the dynamics of quantum correlations.

Giulio Chiribella

Jakob Kaltoft Søndergaard, René Bødker Christensen, Petar Popovski

Distributed quantum protocols rely on classical feedforward information to process measurement outcomes, but heterogeneous hardware and uncertain local timing can make the causal order of measurements ambiguous when inferred solely from arrival times. Even in simple line networks with only Pauli measurements, end nodes cannot distinguish whether a missing outcome is caused by slow measurement or by delayed classical propagation. To resolve this ambiguity, we propose a time-division architecture for quantum networks in which nodes perform measurements in pre-assigned slots, ensuring a unique causal interpretation of outcomes. We formalize this temporal framework and derive the feedforward and adjacency constraints required to preserve measurement causality. For simple network topologies, we present an algorithm that yields optimal measurement schedules. Overall, the proposed time-division model provides a practical coordination layer that bridges the classical network timing with quantum measurement processing, enabling reliable and scalable measurement-based quantum networking.

James T. Cushing